Employing different loss functions for the classification of images via supervised learning

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions. Corresponding dual problems are then derived for different loss functions. The theoretical results are applied by numerically solving a classification task using high dimensional real-world data in order to obtain optimal classifiers. The results demonstrate the excellent performance of support vector classification for this particular problem.     

Di­carbonyl­(tropolonato)­rhodium(I), a redetermination

The mol­ecules of the title complex, [Rh(Trop)(CO)₂] (Trop is 2‐hydroxycyclo­hepta‐2,4,6‐trienonate, C₇H₅O₂), exhibit symmetrical but non‐crystallographic square‐planar molecular geometry, with Rh—C distances of 1.825 (10) and 1.826 (9) Å, Rh—O distances of 2.021 (5) and 2.032 (5) Å, and an O—Rh—O bite angle of 79.4 (2)°. Strong Rh⋯Rh and Rh⋯C intermolecular interactions of 3.683 (3) and 3.650 (5) Å, respectively, are also observed.     

Duality for location problems with unbounded unit balls

Given an optimization problem with a composite of a convex and componentwise increasing function with a convex vector function as objective function, by means of the conjugacy approach based on the perturbation theory, we determine a dual to it. Necessary and sufficient optimality conditions are derived using strong duality. Furthermore, as special case of this problem, we consider a location problem, where the “distances” are measured by gauges of closed convex sets. We prove that the geometric characterization of the set of optimal solutions for this location problem given by Hinojosa and Puerto in a recently published paper can be obtained via the presented dual problem. Finally, the Weber and the minmax location problems with gauges are given as applications.     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

Polymers of carbonic acid 32: Influence of catalysts on propagation and cyclization in the interfacial polycondensation of bisphenol A with diphosgene

Bisphenol A was polycondensed with diphosgene in a dichloromethane/aqueous NaOH system. Temperature, time, and molar ratios of the reactants were optimized according to a previously elaborated optimization of the hydrolytic polycondensation of bisphenol A bischloroformate. Five of the following catalysts were examined: triethylamine, 4‐(N,N‐dimethylamino)pyridine (DMAP), ethyldiisopropylamine (EDPA), tetrabutylammonium hydrogen sulfate, and triethylbenzylammonium chloride (TEBA‐Cl). Triethylamine and DMAP accelerated the hydrolysis of diphosgene by formation of a hydrophilic acylammonium salt. Therefore, the molecular weights decreased with higher concentration of these tert‐amines. However, the molecular weights increased (weight‐average molecular weight up to 10⁶) with higher concentrations of tetraalkylammonium salts because these catalysts favor chain growth in the organic phase via “naked” phenoxide ions without catalyzing the hydrolysis of diphosgene. EDPA gave poor results under all circumstances. Cyclic polycarbonates were discovered in all samples. Their fraction increased with the average molecular weight of the samples. When samples prepared with triethylamine or TEBA‐Cl were fractionated, cycles having molar masses up to 15,000 Da were detected by matrix‐assisted laser desorption/ionization time‐of‐flight mass spectroscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 890–904, 2003     

Determination of Soot Particle Size in a Premixed Flame: a Static and Dynamic Light Scattering Study

In this contribution we report upon our static and dynamic light scattering experiments to characterize soot particles in flames. We studied sooting laminar premixed flame with acetylene as fuel mixed with air as oxidizer. The air equivalence ratio of the combustion was larger than one. We used a Kaskan type burner with circular geometry and a stabilizing flow of nitrogen around the flame. We focused on the determination of the size of the soot particles in the center of the flame as a function of height above burner. In addition we investigated the influence of the mixing ratio of the gases on the size of the particles. Our results show that static light scattering is better suited than dynamic light scattering for a fast and reliable characterization of soot particles in flames. The latter needs detailed a priori information about the flame to allow the unique determination of sizes from the diffusion measurements. The soot particles grow monotonously with height above burner and with decreasing air equivalence ratio. The aggregates have a fractal dimension lower than two.     

Spectral functions at small energies and the electrical conductivity in hot quenched lattice QCD

In lattice QCD, the maximum entropy method can be used to reconstruct spectral functions from Euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and gives a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.